2) Let \(0<p<1\) . Note that \(K\in L^1(\mu )\)  Since \(H^p(\mathbb {D})\)  is an \(F\) -space and the dual \(H^p(\mathbb {D})^*\)  separates the points of \(H^p(\mathbb {D})\)  [1]}, Theorem II.2.7 in [2]} shows that \(\mathcal {H}_{K,\mu }\)  is bounded on \(H^p(\mathbb {D})\)  if and only if a linear functional \(l\circ \mathcal {H}_{K,\mu }\)  belongs to \(H^p(\mathbb {D})^*\)  for each \(l\in H^p(\mathbb {D})^*\) .
